Optimal Design of Acceptance Sampling Plans by Variables for Nonconforming Proportions When the Standard Deviation Is Unknown

This article presents an optimization-based approach for the design of acceptance sampling plans by variables for controlling nonconforming proportions when the standard deviation is unknown. The variables are described by rigorous noncentral Student’s t-distributions. Single and double acceptance sampling (AS) plans are addressed. The optimal design results from minimizing the average sampling number (ASN), subject to conditions holding at producer’s and consumer’s required quality levels. The problem is then solved employing a nonlinear programming solver. The results obtained are in close agreement with previous sampling plans found in the literature, outperforming them regarding the feasibility.

[1]  J. Seinfeld,et al.  Numerical solution of the dynamic equation for particulate systems , 1978 .

[2]  John Shade,et al.  Acceptance Sampling in Quality Control , 2011 .

[3]  W. C. Guenther.  Evaluation of probabilities for the noncentral distributions and the difference of two T-variables with a desk calculator , 1978 .

[4]  Pedro M. Saraiva,et al.  An optimization‐based framework for designing acceptance sampling plans by variables for non‐conforming proportions , 2010 .

[5]  Henry P Goode,et al.  Sampling inspection by variables , 1954 .

[6]  W. Krumbholz,et al.  The operating characteristic of double sampling plans by variables when the standard deviation is unknown , 2006 .

[7]  Thomas Rbement,et al.  Fundamentals of quality control and improvement , 1993 .

[8]  James R. Evans,et al.  Total Quality: Management, Organization, and Strategy , 1993 .

[9]  Arne Drud,et al.  CONOPT: A GRG code for large sparse dynamic nonlinear optimization problems , 1985, Math. Program..

[10]  Irene A. Stegun,et al.  Handbook of Mathematical Functions. , 1966 .

[11]  Chi-Hyuck Jun,et al.  Multiple dependent state sampling plans for lot acceptance based on measurement data , 2007, Eur. J. Oper. Res..

[12]  D. Sommers.  Two-Point Double Variables Sampling Plans , 1981 .

[13]  H. C. Hamaker,et al.  Acceptance Sampling for Percent Defective by Variables and by Attributes , 1979 .

[14]  A. Blanton Godfrey,et al.  Reviews of Standards and Specifications: Tables for the Construction of Matched Single, Double, and Multiple Sampling Plans with Application to MIL-STD-105D , 1980 .

[15]  Dean V. Neubauer,et al.  Acceptance Sampling in Quality Control , 1983 .

[16]  Russell V. Lenth,et al.  Cumulative Distribution Function of the Noncentral T Distribution , 1989 .

[17]  W. Krumbholz,et al.  ASN-minimax double sampling plans for variables , 2002 .

[18]  M. Hilbert.  Zweifache ASN-Minimax-Variablenprüfpläne für normalverteiltes Merkmal bei unbekannten Parametern , 2005 .

[19]  W. A. Wallis,et al.  Techniques of Statistical Analysis. , 1950 .

[20]  G. B. Wetherill,et al.  Quality Control and Industrial Statistics , 1975 .